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105 LearnersLast updated on September 20, 2025
GCF of 16 and 19
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share the items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 16 and 19.
What is the GCF of 16 and 19?
The greatest common factor of 16 and 19 is 1. The largest divisor of two or more numbers is called the GCF of the number. If two numbers are co-prime, they have no common factors other than 1, so their GCF is 1.
The GCF of two numbers cannot be negative because divisors are always positive.
How to find the GCF of 16 and 19?
To find the GCF of 16 and 19, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 16 and 19 by Using Listing of Factors
Steps to find the GCF of 16 and 19 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 16 = 1, 2, 4, 8, 16.
Factors of 19 = 1, 19.
Step 2: Now, identify the common factors of them Common factor of 16 and 19: 1.
Step 3: Choose the largest factor The largest factor that both numbers have is 1.
The GCF of 16 and 19 is 1.
GCF of 16 and 19 Using Prime Factorization
To find the GCF of 16 and 19 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 16: 16 = 2 × 2 × 2 × 2 = 24
Prime Factors of 19: 19 is a prime number, so its only prime factor is 19.
Step 2: Now, identify the common prime factors There are no common prime factors.
Step 3: The GCF is the product of the lowest power of all common prime factors. Since there are no common prime factors, the GCF is 1.
The Greatest Common Factor of 16 and 19 is 1.
GCF of 16 and 19 Using Division Method or Euclidean Algorithm Method
Find the GCF of 16 and 19 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 19 by 16 19 ÷ 16 = 1 (quotient),
The remainder is calculated as 19 − (16×1) = 3
The remainder is 3, not zero, so continue the process
Step 2: Now divide the previous divisor (16) by the previous remainder (3)
Divide 16 by 3 16 ÷ 3 = 5 (quotient), remainder = 16 − (3×5) = 1
The remainder is 1, not zero, so continue the process
Step 3: Now divide the previous divisor (3) by the previous remainder (1)
Divide 3 by 1 3 ÷ 1 = 3 (quotient), remainder = 3 − (1×3) = 0
The remainder is zero, so the divisor will become the GCF.
The GCF of 16 and 19 is 1.
Common Mistakes and How to Avoid Them in GCF of 16 and 19
Finding the GCF of 16 and 19 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
Mistake 1
Listing Incorrect Factors
Students may sometimes list incorrect factors.
For example, while listing factors of 16, students may mention 10, which is incorrect. To avoid this, students should carefully divide the number and list the factors correctly.
Mistake 2
Choosing the wrong common factor
Students may sometimes select the smallest common factor instead of the largest one. For the GCF of 16 and 19, the largest common factor is 1. Understanding that 1 is the only common factor in certain cases is key.
Mistake 3
Forgetting to include 1 as a factor
Sometimes students may forget 1 as a common factor of the numbers. Although it does not affect the GCF in this case, it indicates incomplete understanding of factors. Students should include 1 as a factor.
Mistake 4
Using Multiples instead of factors
Students confuse factors with multiples. In that confusion, they may write multiples instead of factors. To avoid this confusion, students should know the definitions of multiples and factors clearly.
Mistake 5
Assuming GCF is always greater than 1
Students may assume that the GCF of two numbers is always greater than 1. But if two numbers are co-prime, their GCF is 1. Understanding the concept of co-prime numbers is important.
Greatest Common Factor of 16 and 19 Examples
Problem 1
A teacher has 16 apples and 19 oranges. She wants to group them into equal sets, with the largest number of items in each group. How many items will be in each group?
We should find the GCF of 16 and 19.
The GCF of 16 and 19 is 1.
There are 1 equal group. 16 ÷ 1 = 16 19 ÷ 1 = 19
There will be 1 group, and each group gets 16 apples and 19 oranges.
Explanation
As the GCF of 16 and 19 is 1, the teacher can make one group.
Now divide 16 and 19 by 1.
Each group gets all 16 apples and 19 oranges.
Problem 2
A school has 16 red chairs and 19 blue chairs. They want to arrange them in rows with the same number of chairs in each row, using the largest possible number of chairs per row. How many chairs will be in each row?
The GCF of 16 and 19 is 1. So each row will have 1 chair.
Explanation
There are 16 red and 19 blue chairs.
To find the total number of chairs in each row, we should find the GCF of 16 and 19.
Each row will have 1 chair.
Problem 3
A tailor has 16 meters of red ribbon and 19 meters of blue ribbon. She wants to cut both ribbons into pieces of equal length, using the longest possible length. What should be the length of each piece?
For calculating the longest equal length, we have to calculate the GCF of 16 and 19.
The GCF of 16 and 19 is 1.
Each piece of ribbon will be 1 meter long.
Explanation
For calculating the longest length of the ribbon, first, we need to calculate the GCF of 16 and 19, which is 1.
The length of each piece of ribbon will be 1 meter.
Problem 4
A carpenter has two wooden planks, one 16 cm long and the other 19 cm long. He wants to cut them into the longest possible equal pieces, without any wood left over. What should be the length of each piece?
The carpenter needs the longest piece of wood. The GCF of 16 and 19 is 1. The longest length of each piece is 1 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 16 cm and 19 cm, respectively, we have to find the GCF of 16 and 19, which is 1 cm.
The longest length of each piece is 1 cm.
Problem 5
If the GCF of 16 and ‘b’ is 1, and the LCM is 304, find ‘b’.
The value of ‘b’ is 19.
Explanation
GCF × LCM = product of the numbers
1 × 304 = 16 × b
304 = 16b
b = 304 ÷ 16 = 19
FAQs on the Greatest Common Factor of 16 and 19
1.What is the LCM of 16 and 19?
2.Is 16 divisible by 4?
3.What will be the GCF of any two co-prime numbers?
4.What is the prime factorization of 19?
5.Are 16 and 19 prime numbers?
Important Glossaries for GCF of 16 and 19
- Factors: Factors are numbers that divide a target number completely. For example, the factors of 16 are 1, 2, 4, 8, and 16.
- Co-prime Numbers: Two numbers are co-prime if their GCF is 1. For example, 16 and 19 are co-prime.
- Prime Factors: These are the factors of a number that are prime numbers and divide the given number completely. For example, the prime factors of 16 are all 2s.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 16 and 19 is 304.
- Remainder: The value left after division when a number cannot be divided evenly. For example, when 19 is divided by 16, the remainder is 3.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
